23. (10) In an ideal LC circuit the resistance is 0 and there is no energy dissi

Question

23. (10) In an ideal LC circuit the resistance is 0 and there is no energy dissipation. A 6.00pF capacitor is charged fully by a 12V DC battery. This capacitor is connected to an inductor of inductance L 25mll. a. Calculate the angular frequency, o, the frequency, f and the period of the oscillation, T Switch closes at 1-0. Initial charge Qo b. For the above LC circuit determine the initial charge on the capacitor, Qa, and the maximum current Imax in the circuit. c Calculate the maximum energy stored in the capacitor and the maximum energy stored in the magnetic field of the inductor.

Explanation / Answer

(a)

angular frequency w = 1/sqrt(LC)

w = 1/sqrt(25*10^-3*6*10^-6)

w = 2582 s^-1

frequency f = w/(2pi) = 2582/(2*pi) = 411 Hz

period of the oscillation T = 1/f = 0.00243 s

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part(b)

Qo = C*V

Qo = 6*10^-6*12

Qo = 72*10^-6 C

Imax = V*w*C

Imax = 12*2582*6*10^-6 = 0.186 A

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part(c)

maximum energy stored in capacitor Emax = (1/2)*C*v^2 = (1/2)*6*10^-6*12^2 = 0.000432 J

maximum energy stored in inductorr Emax = (1/2)*L*Imax^2 = (1/2)*25*10^-3*0.186^2 = 0.000432 J

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